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Summer school II: Summer school on singular Kählerian metrics and Hermitian geometry

08/11/2025 - 08/15/2025
Rényi Institute, Main Lecture Hall

Description

The  "Summer school on singular Kählerian metrics and Hermitian geometry" will be held between 11-15 August 2025, at the main lecture hall of the Rényi Institute (Budapest), as part of the thematic semester Complex analysis and Geometry (August-December 2025) hosted by the Erdős center. Advanced PhD students , postdocs, and junior researchers working in complex geometry are encouraged to apply. 
 
During this one week summer school, Hans-Joachim Hein (Münster) and Daniele Angella (Firenze) will give series of talks on recent advances on singular Kähler metrics, and Hermitian geometry respectively. We expect that the audience will consist of advanced graduate students, postdocs and junior faculty working in complex geometry. 
 
MINICOURSES

Daniele Angella: Cohomological properties and Hermitian metrics of complex non-Kähler manifolds

Tutor: Nicoletta Tardini

Abstract:  the first lectures will provide a survey of the cohomological properties and topological aspects of complex manifolds, as well as canonical metrics on complex manifolds. We will then focus on some analytic problems concerning the geometry of the Chern connection on Hermitian manifolds, such as the existence of metrics with constant Chern-scalar curvature, generalizations of the Kähler-Einstein condition to the non-Kähler setting, the convergence of the Chern-Ricci flow on compact complex surfaces, and the asymptotic behavior of Monge-Ampère volumes of Hermitian metrics in the ddc-class.

Hans-Joachim Hein:  Liouville theorems and Evans-Krylov estimates for the complex Monge-Ampère equation

Tutor: Yifan Chen

Abstract: A classical idea going back at least to work of Leon Simon (1997) is that Liouville theorems for solutions to elliptic or parabolic PDEs are equivalent to Schauder-type regularity estimates. The goal of this course is to describe some recent developments of this idea concerning the regularity of the complex Monge-Ampère equation with respect to singular reference metrics. We will start with a quick look at Yau's C^2 and C^3 estimates and then present a new proof of the Evans-Krylov C^{2,alpha} estimate on a Euclidean ball. Based on this we will consider the case of singular backgrounds such as cylinders and cones, discussing some parts of my recent joint work with V. Tosatti and M.-C. Lee and work of my former student J. Klemmensen.

REGISTRATION
The registration period has ended.

 

ACCOMMODATION

Limited financial support for accommodation is available for students and postdocs. 

LOCAL EXPENSES

Apart from the above support in accommodation, we cannot cover local expenses.

IMPORTANT INFORMATION

The conference organizers do not authorize any external subjects to arrange or propose accommodation for the participants. If you receive e-mails from travel or housing agencies, etc., containing booking offers and requests for sending your personal data or advance payment, you should treat them as scams.

All official communications will only come from the Erdős Center secretary or directly from the organizers. Those who requested financial support for the accommodation will get the details directly from the secretary of the Erdős Center.

Venue:  Main Lecture Hall, Rényi Institute

https://maps.app.goo.gl/RxdVNyhTAYXbzS2V8

The following link gives practical information (e.g. local traveling):

https://erdoscenter.renyi.hu/practicalities


 Schedule

The schedule of the summer school and the schedule of the  lightning talks and  posters are available in Downloads below.

Organizers

Tamás Darvas (University of Maryland)
Gergely Kiss (Rényi Institute)
László Lempert (Purdue University)
Gábor Székelyhidi (Northwestern University)
Róbert Szőke (Eötvös L. University-Rényi Institute)
Adriano Tomassini (Università di Parma)

Invited Speakers

Daniele Angella (Università di Firenze)
Hans-Joachim Hein (Universität Münster)

Participants